Using a three-dimensional hydrodynamic simulation of the collision and an equation of state containing a first order phase transition to the quark-gluon plasma, we study thermal photon production for Au+Au collisions at E_lab=11.5 AGeV and for Pb+Pb collisions at 160 AGeV. We obtain surprisingly high rates of thermal photons even at the lower energy, suggesting that, contrary to what was expected so far, photon production may be an interesting topic for experimental search also at the

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... g Gradient Synchrotron. When applied to the reaction S+Au at 200 AGeV, our model can reproduce preliminary data obtained by the WA80 Collaboration without having to postulate the existence of an extremely long-lived mixed phase as was recently proposed.